4.1.1 The
                                 thickness, t, of semi-ellipsoidal and hemispherical unstayed
                                 ends, and the knuckle section of torispherical ends, dished from plate,
                                 having pressure on the concave side and satisfying the conditions
                                 listed below, is to be determined by the following formula:
                                 
                              
                              
                              
                              
                              
                              
                              
                              
                            
                           
                           
                           
                              
                              
                              4.1.2 For
                                 semi-ellipsoidal ends:
                              
                              
                              
                              
                              the external height, H ≥ 0,18Do
                                 
                              
                              
                              
                              
                                 
                                    where
                                    
                                       | 
                                                
                                             D
                                             o
                                              | 
                                       = | 
                                       the external diameter of the parallel portion of the end, in
                                             mm. | 
                                    
                                 
                               
                              
                              
                            
                           
                           
                           
                              
                              
                              4.1.3 For
                                 torispherical ends:
                              
                              
                              
                              
                              the internal radius, Ri ≤ Do
                                 
                              
                              
                              
                              
                              the internal knuckle radius, ri ≥ 0,1Do
                                 
                              
                              
                              
                              
                              the internal knuckle radius, ri ≥ 3t
                                 
                              
                              
                              
                              
                              the external height, H ≥ 0,18Do, and is determined
                                 as follows: 
                              
                              
                              
                              
                              
                            
                           
                           
                           
                              
                              
                              4.1.4 In
                                 addition to the formula in Pt  5, Ch  11,  4.1 Minimum thickness 4.1.1 the
                                 thickness, t, of a torispherical head, made from more
                                 than one plate, in the crown section, is to be not less than that
                                 determined by the following formula:
                                 
                              
                              
                              
                              
                              
                              
                              
                              
                            
                           
                           
                           
                           
                           
                           
                           
                           
                           
                              
                              
                              4.1.7 The minimum thickness of the head, t, is in no case to be less than
                                 3 + 
 mm, where Di is as defined in Pt  5, Ch  11,  1.2 Definition of symbols. The
                                 minimum thickness permitted for vessels manufactured in corrosion resistant steels will
                                 be the subject of special consideration. 
                              
                              
                              
                            
                           
                           
                           
                              
                              
                              4.1.8 For
                                 ends which are butt welded to the drum shell, see 
                                 Pt  5, Ch  11,  1.9 Joint factors, the thickness of the edge of
                                 the flange for connection to the shell is to be not less than the
                                 thickness of an unpierced seamless or welded shell, whichever is applicable,
                                 of the same diameter and material and determined by Pt  5, Ch  11,  2.1 Minimum thickness.